Unobserved heterogeneity in auctions under restricted stochastic dominance

We study the identification of first-price auctions with nonseparable unobserved heterogeneity. In particular, we extend Hu et al. (2013) by relaxing the first-order stochastic dominance condition. Instead, we assume restricted stochastic dominance relations among value quantile functions and show that the same relations pass to bid quantile functions. An ordered tree summarizes these relations and provides a total ordering. Relying on the proposed restricted stochastic dominance ordering, we extend a list of identification results in the empirical auction literature.